On the Solution of Topological Landau-Ginzburg Models with $c=3$

TL;DR

This paper solves a specific topological Landau-Ginzburg model with central charge c=3, using flatness conditions to derive key relations, and extends the approach to a different model, providing insights into their structure.

Contribution

It introduces a simplified method based on metric flatness to solve topological Landau-Ginzburg models, including the c=3 case and an alternative model.

Findings

Derived the differential equation relating af to the flat coordinate t.

Applied the method successfully to the x^3 + y^6 model.

Provided solutions at the limit of traditional consistency techniques.

Abstract

The solution is given for the $c=3$ topological matter model whose underlying conformal theory has Landau-Ginzburg model $W=-\qa (x^4 +y^4)+\af x^2y^2$. While consistency conditions are used to solve it, this model is probably at the limit of such techniques. By using the flatness of the metric of the space of coupling constants I rederive the differential equation that relates the parameter \af\ to the flat coordinate $t$. This simpler method is also applied to the $x^3+y^6$-model.